903 B

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id	title	challengeType	forumTopicId	dashedName
5900f4e61000cf542c50fff9	Problem 378: Triangle Triples	5	302040	problem-378-triangle-triples

--description--

Let T(n) be the n^{\text{th}} triangle number, so T(n) = \frac{n(n + 1)}{2}.

Let dT(n) be the number of divisors of T(n). E.g.: T(7) = 28 and dT(7) = 6.

Let Tr(n) be the number of triples (i, j, k) such that 1 ≤ i < j < k ≤ n and dT(i) > dT(j) > dT(k). Tr(20) = 14, Tr(100) = 5\\,772 and Tr(1000) = 11\\,174\\,776.

Find Tr(60\\,000\\,000). Give the last 18 digits of your answer.

--hints--

triangleTriples() should return 147534623725724700.

assert.strictEqual(triangleTriples(), 147534623725724700);

--seed--

--seed-contents--

function triangleTriples() {

  return true;
}

triangleTriples();

--solutions--

// solution required

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